Long Division with Large Numbers Worksheets
Long division is a technique and strategy that we use to find the quotient of much larger values. As we progress to working with larger values which are found all throughout the real world this technique will become very commonplace. In this section we take long division to a whole new level. Previously we were working two-digit values into three-digit values. We now amp it up to work on five and six-digit values both in forms as divisors and dividends. While this may seem very complicated, at first, you will quickly realize it same form of math, just more of it. Your main goal here should just be to stay organized and give yourself plenty of room to work with. I encourage students to use one sheet of scrap paper per problem, at first.
Aligned Standard: Grade 6 Numbers - 6.NS.B.2
- Long Division Step-by-step Lesson- I haven't taught sixth grade in a while. I forgot how long some of these problems can take. This lesson asks: Is 634,450 divisible by 25?
- Guided Lesson - I give you three different ways to look and approach these types of problems. We also look at a word problem that we pull this type of problem out of.
- Guided Lesson Explanation - It took four pages to fully explain three problems. You can see why some kids get frustrated with this skill.
- Practice Worksheet - A nice mix and rhythm of the same problem types. We are look at hard and soft values.
- Double Digit Long Division Five Pack - Find all the quotients that you can. This is a pack of fifty problems for you.
- Matching Worksheet - Match the question to the outcome of its quotient.
- Answer Keys - These are for all the unlocked materials above.
I started throwing in more word problems to lead to the problems (specifically sheet 2).
- Homework 1 - Use an arrow to help you like this example shows you.
- Homework 2 - Christina has 1840 blocks. If she shares them with 23 friends, how many blocks does each friend get?
- Homework 3 - There are 58 students in a class and 5,046 toffees. If the toffees are divided equally, how many will each student get?
I tried to make these very clean and simple to help students progress on their own.
- Practice 1 - See if you can spot the pattern in the divisors of these problems.
- Practice 2 - There are 3763 bottle caps in Peter’s bottle cap collection. If the bottle caps are organized into 71 groups, how big is each group?
- Practice 3 - We step it up to five digits for you and walk you through the answer in the walk through solution that is provided for you.
Math Skill Quizzes
I made these challenging, yet very doable for younger middle schoolers.
- Quiz 1 - These are straight up problems with division.
- Quiz 2 - More fair and balanced problems for you to work through.
- Quiz 3 - Some of these problems are pretty tough.
Tips for Long Division of Large Numbers
When you start learning division, the problems are very simple. You come across things like dividing 20 by 5, and you get an answer of 4. And unlike every other operation where you go from the right-hand side; long division moves from left to right. For each number you are dividing, you get to complete a series of division, multiplication, and subtraction. With some easy tips, you can nail the division of these numbers quickly.
My first piece of advice is very ordinary, just draw yourself a picture anytime you can. As you know division is the process of separating things into groups. Why not do this. This is not always practical when working with large values, but they can help keep you on task.
Here are steps that I would encourage you to use when processing the calculations for these problems. Once you get in the habit of doing this, it almost becomes automatic.
Step 1) Write the dividend inside the division symbol and the divisor outside it. Place a horizontal bar directly over the dividend which creates and area for you to slowly start to flesh out the quotient.
Step 2) Starting from the far-right digit divide one digit from the divisor into the dividend at a time and subtracting it from the original digit. Make sure to complete the difference and write it out.
The most important thing to keep in mind with these is to always stay organized. Give yourself plenty of writing space and do not cram things together. Spacing is very important so that you can follow along properly. Make sure everything is appropriately aligned and take your time with each problem. These are not math facts you are dealing with that will require you to do them carefully. As you get the rhythm of these problems, your speed with calculating them will pick up.
Simple Advice for When You Are Confronted with These Types of Problems
When you are working with these types of problems there is one simple piece of advice that I can offer and that is to stay organized. In most case the basic operation is not difficult at all, it is just time consuming. When we are tasked with longer projects, we tend to get lazy. If you write clearly and give yourself enough space to work with, this will be not that difficult of a task for you. Another place that students create difficulty for themselves is number alignment. Make sure to center everything that you write as much as possible. Also, circle or in some way signify your trailing working problem, if things get cramped in the space you are working with.